This paper details the key steps in Kant’s transcendental proof that we perceive, not merely imagine, physical objects. These steps begin with Kant’s method (§II) and highlight the spatio-temporal character of our representational capacities (§III), Kant’s two transcendental proofs of mental content externalism (§IV), his proof that we can only make causal judgments about spatial substances (§§V, VI), the transcendental conditions of our self-ascription of experiences (§VII), Kant’s semantics of singular cognitive reference (§VIII), perceptual synthesis (§IX), Kant’s justificatory fallibilism (§X), and the cognitive transcendence of global perceptual hypotheses (§XI). The proof outlined here differs markedly from ‘analytic transcendental arguments’ that focus selectively on Kant’s ‘Refutation of Idealism’ and portions of the ‘Transcendental Deduction of the Pure Concepts of the Understanding’. Understood as presented here, Kant’s epistemology is directly relevant to contemporary philosophical issues